Question

the following table shows the steps involved in solving a linear equation. which of the following properties correctly fills in the missing step used to get the equation in its corresponding form?

equation	steps
?	addition property of equality
$60 = 9x$	multiplication property of equality
$\frac{20}{3} = x$	division property of equality
$x = \frac{20}{3}$	symmetric property of equality

show your work here

$\circ$ $12 = 9x + 5$ $\circ$ $12 = \frac{9x}{5}$

$\circ$ $12 = 9x - 5$ $\circ$ $12 = 5(9x)$

Explanation:

Step1: Recall the Addition Property of Equality

The addition property of equality states that if we add the same number to both sides of an equation, the equation remains true. For the original equation \(4=\frac{9x}{5}-8\), we want to eliminate the \(-8\) on the right - hand side. So we add 8 to both sides.

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LATEXBLOCK0
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Step2: Match with the Given Options

Now we look at the options. The equation we got after applying the addition property of equality is \(12=\frac{9x}{5}\), which matches the second option.

Answer:

\(12 = \frac{9x}{5}\) (the option " \(12=\frac{9x}{5}\)")